Question

A triangle has sides A, B, and C. If the angle between sides A and B is `(3pi)/8`, the angle between sides B and C is `(7pi)/12`, and the length of B is 3, what is the area of the triangle?

Answer 1

`Area ~~ 30.766" units"^2" "`to 3 dp

Explanation:

Sum of internal angles for a triangle is `180^o-> pi" radians"`

So `/_AC= 1/24 pi ->7 1/2color(white)(.)^o`

`h=Bsin(/_AB) = 3 sin(3/8 pi) ~~2.7716`

`" "A/sin(/_BC)=B/sin(/_AC)`

`=> A = (Bsin(/_BC))/sin(/_AC)~~22.201`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`Area = A/2xxh`

`Area = (Bsin(/_BC))/(2sin(/_AC))xxBsin(/_AB)`

`Area = (3sin(/_BC))/(2sin(/_AC))xx3sin(/_AB) ~~ 30.766" "`to 3 dp